How to create Quarter Cylinder
Although there are many ways to do so, you CAN create a quarter cylinder from a cube:


Select the cube object, Go to Edit mode;
Ctrl + B to bevel the selected edge, roll the mouse wheel to adjust segements;
A + A to select all vertices, then W -> Remove Doubles.






Tip:

To ensure the maximum bevel extent on that edge, you can consider either one of the following ways:


After pressing Ctrl + B, you can see the available operations on the 3D View header (with shortcuts). So, you can then press M three times to switch bevel mode to Percent, then type 100 for a maximum Offset percent.





You can also do it after confirming the bevel operation, from either the lowerleft of the Tooblar (T) or a seperate popup menu(F6):